Question

The sum of the digits of a two digit number is 13.The number obtained by interchanging the digits exceed the original number by 9 . Find the number.​

Answer 1

☆ Solution ☆

Given :-

• The sum of the digits of a two digit number is 13 .
• The number obtained by interchanging the digits exceed the original number by 9 .

To Find :-

• The number.

Step-by-Step-Explaination :-

Let the tens place be x and unit place be y

x + y = 13 ...........eq ( 1 )

Original number = 10x + y

By intercganging the digits = 10y + x

( 10x + y ) - ( 10y + x ) = 9

10y + x - 10x + y = 9

10y - y - 10x - x = 9

9y - 9x = 9

9 ( y - x ) = 9

y - x = 1

( 13 - x ) - x = 1 .....using eq ( 1 )

13 - 2x = 1

2x = 12

x = 12/2

x = 6

y = 13 - 6

y = 7

Hence,

The number is 67